The Behaviour of a Process Zone at the Root of a Deep Sharp Flaw for Mode I Loading

2003 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Process Zone ◽  
Fracture Initiation ◽  
Radius Of Curvature ◽  
Mode I ◽  
Zone Size ◽  
Mode Iii ◽  
Root Radius ◽  
Mode I Loading ◽  
Linear Behaviour

The process zone representation of non-linear behaviour at the root of a flaw or crack is frequently used to quantify fracture initiation scenarios. In a paper presented at the 2002 PVP Conference, the author showed that with regard to a process zone at the root of a deep sharp flaw for Mode III loading conditions, its behaviour can be described, to a good degree of accuracy, by inputting the stress distribution ahead of the actual flaw root into an analysis of a process zone at the root of a semi-infinite crack in an infinite solid. The present paper describes an analysis of the analogous Mode I loading situation, with the results being compared with those obtained by a procedure which blends the small and large s/ρ behaviours where s is the process zone size and ρ is the flaw root radius of curvature.

The Mode I Elastic Stress Distribution Near the Root of a Deep Notch With a Parabolic Root Profile

2007 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Elastic Stress ◽  
Notch Root ◽  
Peak Stress ◽  
Fracture Initiation ◽  
Radius Of Curvature ◽  
Mode I ◽  
Mode Iii ◽  
Root Radius ◽  
Notch Root Radius

The basis of a fracture mechanics type methodology for fracture initiation at a blunt notch is the elastic stress distribution immediately ahead of a notch root. Earlier work, presented at the 2006 ASME PVP Conference [7], for the Mode III deformation of a deep notch with a parabolic root profile, has shown that the shear stress σ(x) at a distance x ahead of the root is uniquely defined by the peak stress σp, x and ρ (the notch root radius of curvature), when x and ρ are both small compared with the notch depth, irrespective of the loading characteristics and the notch shape away from the root. This paper is concerned with the corresponding Mode I deformation situation, with the objective of providing support for the viability of a similar conclusion for Mode I deformation.

The Mode III Elastic Stress Distribution Near the Root of a Deep Sharp Notch With a Parabolic Root Profile

2006 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Elastic Stress ◽  
Notch Root ◽  
Peak Stress ◽  
Fracture Initiation ◽  
Radius Of Curvature ◽  
Mode Iii ◽  
Root Radius ◽  
Notch Root Radius ◽  
Starting Point

In developing a fracture initiation methodology for blunt notches, the basic starting point is the elastic stress distribution immediately ahead of a notch root. Earlier work for Mode III deformation of a two-dimensional blunt notch has shown that the shear stress immediately ahead of the notch root (i.e. at a distance small compared with the notch root radius of curvature) is dependent on the peak stress and notch root radius, but is independent of the notch shape and the loading characteristics. However there are many situations, i.e. with sharp notches, where we are interested in the stress at a distance that is not necessarily small compared with the notch root radius. Thus this paper shows that with a notch that has a parabolic root profile, when this distance and the notch root radius are both small compared with the notch depth, then the stress at this distance is again dependent on the peak stress and notch root radius, but is independent of the notch shape away from the root and the loading characteristics.

Improved Failure Assessment Diagrams to Describe Delayed Hydride Cracking Initiation at a Blunt Flaw

2003 ◽  
Author(s):  
Douglas A. Scarth ◽  
Ted Smith
Keyword(s):  
Process Zone ◽  
Peak Stress ◽  
Mode I ◽  
Mode Iii ◽  
Exact Relation ◽  
Practical Applications ◽  
Failure Assessment ◽  
Mode I Loading ◽  
Delayed Hydride Cracking ◽  
Hydride Cracking

Delayed Hydride Cracking (DHC) in Zr-2.5 Nb alloy material is of interest to the CANDU (CANada Deuterium Uranium) industry in the context of the potential to initiate DHC at a blunt flaw in a CANDU nuclear reactor pressure tube. The material is susceptible to DHC when a hybrided region forms at the flaw tip. The hydrided region could then fracture to the extent that a crack forms, and is able to grow by the DHC crack growth mechanism. A process-zone based methodology for evaluation of DHC initiation at a blunt flaw that takes into account flaw geometry has been developed. In a paper presented at the 2000 ASME PVP Conference, the process-zone methodology was used to develop failure assessment diagrams in such a way that the geometry dependence of the failure assessment curves was minimized. This was achieved by defining the ordinate of the failure assessment diagrams in terms of the ratio of the applied elastic peak stress divided by the threshold peak stress for DHC initiation at the tip of a deep flaw. However, the resultant failure assessment curves for Mode I loading did not have the simple form as the curves for Mode III loading, where the Mode III case was modelled in order to clearly see the interplay between material and geometry parameters. The present paper demonstrates that the irregular shapes of the Mode I curves were due to the relation for the threshold peak stress for the deep flaw that was used in the Mode I failure assessment curves. In the 2000 ASME PVP Conference paper an exact relation for the threshold peak stress was used for Mode III loading, while an approximate relation was used for Mode I. In the present paper a more accurate relation for the threshold peak stress for a deep flaw was used for Mode I loading, and the resultant Mode I failure assessment curves have a simpler form, which leads to more practical applications of the approach. Agreement between the improved Mode I failure assessment diagram predictions and experimental results is reasonable.

The Mode III Elastic Stress Distribution in the Immediate Vicinity of an Inclusion

2005 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Elastic Stress ◽  
Notch Root ◽  
Research Programme ◽  
Local Stress ◽  
Peak Stress ◽  
Radius Of Curvature ◽  
Mode Iii ◽  
Root Radius ◽  
Notch Root Radius

As part of a wide ranging research programme aimed at developing a fracture mechanics methodology for blunt notches, earlier work for a general two-dimensional blunt notch Mode III model has shown that the stress at a distance × ≪ ρ (notch root radius of curvature) ahead of the notch root only depends on x, ρ and the peak stress σp, irrespective of the notch shape and the loading characteristics. This uniqueness has been confirmed for various notch profiles and loading scenarios. In this paper we show that the uniqueness of the local stress distribution is peculiar to a notch and does not apply to an inclusion.

Uniqueness of the Two Extremes Procedure for Quantifying Fracture Initiation at a Blunt Flaw

2007 ◽  
Author(s):  
E. Smith
Keyword(s):  
Process Zone ◽  
Research Programme ◽  
Peak Stress ◽  
Fracture Initiation ◽  
Relative Displacement ◽  
Zone Size ◽  
Complete Spectrum ◽  
Root Radius ◽  
Sharp Crack ◽  
Single Relation

The author is involved in a wide-ranging research programme, whose objective is to extend the sharp crack fracture mechanics methodology to a blunt flaw, so as to take credit for the blunt flaw geometry. The basis of the approach is the process zone representation of the micro-mechanistic processes that are associated with fracture. In earlier work, a blunt flaw fracture initiation relation has been derived, subject to the restriction that the process zone size s is small compared with the flaw depth (length) or any other characteristic dimension, such as remaining ligament width, but not necessarily the flaw root radius ρ. The relation gives the critical elastic flaw-tip peak stress σpcr, and has been derived using a two extremes procedure, whereby the separate σpcr solutions for small and large s/ρ are blended together so as to give a single relation that is valid for the complete spectrum of s/ρ values. Equally well, one can develop a relation for σpcr, based on the separate solutions for vT, the relative displacement across the process zone at the flaw root. For the fracture initiation relation based on separate σpcr solutions to be meaningful, the relation should be close to that based on separate vT solutions. The objective of the work described in the present paper is to demonstrate that the two relations are indeed close to each other.

A comparison between rapid expressions for evaluation of the critical J-integral in plates with U-notches under mode I loading

2011 ◽  
Vol 46 (8) ◽  
pp. 852-865 ◽  
Author(s):  
E Barati ◽  
F Berto
Keyword(s):  
Loading Condition ◽  
Control Volume ◽  
Notch Root ◽  
Critical Value ◽  
Fracture Load ◽  
Mode I ◽  
J Integral ◽  
Root Radius ◽  
Notch Root Radius ◽  
Mode I Loading

In this paper, some practical linear-elastic equations for evaluation of the critical value of the J-integral in plates with U-notches under mode I loading are presented and applied to brittle and quasi-brittle materials. The relationship between the J-integral and strain energy averaged over a well-defined control volume, depending on the static properties of the material, is applied, with the aim of obtaining the final expressions. It is found that these three proposed equations provide the same results, with any differences being negligible. By using one of these equations, one can evaluate Jcr and then predict the critical fracture load by means of the Jcr criterion. The results have shown that the critical value of the J-integral ( Jcr) is a function of the ratio of the material control radius to the notch-root radius ( Rc/ρ), the ratio of specimen width to notch depth ( w/ a), the notch acuity ( a/ρ), and the loading condition (tensile or bending loadings) in U-notches under mode I loading. However, the effect of the loading condition, a/ρ and w/ a ratios may be negligible. Therefore only the Rc/ρ ratio (i.e. the material properties and the notch-root radius of the specimen) affects Jcr.

Fracture Mechanics of Tapered Cracks

2009 ◽  
Author(s):  
Edwin Smith
Keyword(s):  
Fracture Mechanics ◽  
Stress Field ◽  
Fracture Initiation ◽  
Mode I ◽  
Mode I Crack ◽  
Mode Iii ◽  
Singularity Order

The paper shows that for the Mode III loading of a tapered crack whose near tip profile is defined by the relation (y/c) = (x/c)m, the singularity order of the stress field is −1/2, as it is for a linear crack, irrespective of the m value. This result is a generalization of the result reached in an earlier paper by the author, for the particular case m = 3/2. The result’s implications to the quantification of fracture initiation at the root of a Mode I crack are discussed.

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